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A093489 Define the total signature symmetry of a number n to be the number of values r takes such that n-r and n+r have the same prime signature. Sequence contains the total signature symmetry of n. 3
0, 0, 0, 1, 1, 1, 1, 3, 2, 3, 2, 4, 2, 3, 4, 5, 4, 7, 2, 6, 4, 5, 4, 10, 5, 5, 7, 7, 4, 10, 4, 10, 7, 7, 8, 16, 6, 7, 10, 11, 4, 14, 7, 10, 13, 9, 8, 18, 5, 13, 11, 12, 8, 20, 11, 17, 11, 13, 8, 27, 5, 10, 17, 16, 11, 19, 10, 14, 11, 15, 15, 33, 10, 15, 20, 15, 12, 23, 9, 22, 18, 13, 12, 31, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Number of partitions of 2n in two parts with identical prime signatures. Conjecture: (1) No term is zero for n > 3. (2) Every number k appears a finitely many times in the sequence. I.e., for every k there exists a number f(k) such that for all n > f(k), a(n) > k. Subsidiary sequence: the frequency of n.

LINKS

Charlie Neder, Table of n, a(n) for n = 1..1000

EXAMPLE

a(12) = 4. The four values r can take are 1,2,5 and 7, giving the four pairs of numbers with identical prime signatures; (11,13),(10,14),(7,17) and (5,19).

CROSSREFS

Cf. A093488, A093491, A093492.

Sequence in context: A115041 A039641 A198729 * A066919 A268714 A084117

Adjacent sequences:  A093486 A093487 A093488 * A093490 A093491 A093492

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Apr 16 2004

EXTENSIONS

More terms from Joshua Zucker, Jul 24 2006

STATUS

approved

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Last modified October 15 18:04 EDT 2021. Contains 348033 sequences. (Running on oeis4.)